Question

An assembly consists of two mechanical components. Suppose that the probabilities that the first and second components meet specifications are 0.95 and 0.98, respectively. Assume that the components are independent. Determine the probability mass function of the number of components in the assembly that meet specifications.

Answer 1

If you consider that both components are independent one of the other and the assembly consists of a union of both of them, the probability that a random element of the assembly meet specifications can be obtained as the product of their probabilities of meeting their specifications.

`P_(1)=0.95\\P_(2)=0.98\\P_(12)=P_(1)*P_(2)\\`

therefore the probability mass function of the number of components in the assembly are:

`P_(12)=0.931`